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Convergence and stability of implicit methods for jump-diffusion systems. (English) Zbl 1109.65007
The authors consider the strong convergence of implicit methods for the solution of stochastic differential equations with Poissonian jumps. It is demonstrated that implicitness offers benefits for the numerical stability. A mean-square linear stability analysis is undertaken.
MSC:
65C30Stochastic differential and integral equations
65L20Stability and convergence of numerical methods for ODE
34F05ODE with randomness
60H10Stochastic ordinary differential equations
60H35Computational methods for stochastic equations